CN112180324A - Non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring - Google Patents

Non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring Download PDF

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CN112180324A
CN112180324A CN202010959291.2A CN202010959291A CN112180324A CN 112180324 A CN112180324 A CN 112180324A CN 202010959291 A CN202010959291 A CN 202010959291A CN 112180324 A CN112180324 A CN 112180324A
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曾浩威
张小飞
赖欣
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring, which considers non-circular phase information of signals when establishing an algorithm model, and expands a received signal matrix by utilizing the characteristic that the elliptic covariance is not zero so as to achieve the purpose of increasing the spatial degree of freedom; by combining the direct positioning technology and the concept of a Capon algorithm in the direction of arrival estimation, the covariance matrixes of the data received by the positions of the observation stations are comprehensively considered, and the high-precision positioning of the multi-target source can be realized only by one moving observation station; and the problem of high complexity caused by the introduction of the non-circular phase is effectively solved by introducing a dimension reduction idea. The method avoids the problem of matching intermediate parameters and parameters of the traditional two-step method, directly obtains the position information of the target source from the original receiving data layer, and effectively improves the positioning precision; the expansion of the received signal vector increases the spatial degree of freedom of the algorithm, improves the resolution and can simultaneously estimate more information sources.

Description

Non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring
Technical Field
The invention relates to the technical field of passive wireless positioning, in particular to a non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle movement monitoring.
Background
In the existing radiation source positioning method, radiation source signals are mostly regarded as complex circle Gaussian signals, a signal model is too simple, characteristic information of the radiation source signals cannot be fully utilized, and therefore precision is low. When the signal model is established, the algorithm model is designed in a targeted manner by combining the signal characteristics, so that the positioning accuracy of the algorithm can be improved. Non-circular signals are common signal types in modern communication systems, so that the research on a radiation source positioning method aiming at the non-circular signal type has more general practicability and very important practical significance.
The traditional two-step positioning technology needs to estimate intermediate parameters firstly, the existence of an intermediate processing link causes that the intermediate processing link inevitably loses partial position information, and under multiple radiation sources, extra parameter matching is needed before position resolving, so that the asymptotically optimal estimation performance is difficult to obtain, and the practicability is low. The direct positioning technology directly estimates the position of the radiation source from the original received data without additional parameter estimation, thereby effectively avoiding the problem of a two-step positioning system and having higher positioning precision. The direct positioning technology can conveniently utilize original data information, so that the direct positioning technology combined with signal characteristics can obtain better estimation performance. However, the existing direct positioning technology combining signal characteristics is not generally applicable to signal types such as constant modulus signals and cyclostationary signals, does not consider the problem of dimension reduction, and has high algorithm complexity.
Disclosure of Invention
The invention aims to solve the technical problem of providing a non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle movement monitoring aiming at the defects involved in the background technology.
The invention adopts the following technical scheme for solving the technical problems:
a non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring comprises the following steps:
step 1), an unmanned aerial vehicle receives a plurality of non-circular radiation source signals in L different observation time slots and samples the received signals;
step 2), expanding received signal vectors according to the non-circular characteristics of the signal source, respectively calculating expanded covariance matrixes of received signals of different observation time slots, and constructing a cost function by using a Capon algorithm;
step 3), reducing the dimension of the cost function, and converting the non-circular phase dimension reduction problem into a secondary optimization problem; fusing all the extended covariance matrixes, and constructing a cost function after dimension reduction;
and 4) searching the cost function subjected to the dimension reduction to obtain the position of the non-circular radiation source.
As a further optimization scheme of the non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring, the received signal r of the unmanned aerial vehicle at the kth sampling moment of the l observation time slot in the step 1)l(k) Is composed of
Figure BDA0002679862900000021
In the formula, rl(k) Is the received signal vector of the kth sampling moment of the l observation time slot, Q is the number of non-circular radiation sources,
Figure BDA0002679862900000022
for the signal manifold vector of the qth target source to the antenna array in the l observation time slot, sl,q(k) The signal waveform of the qth target source at the kth sampling snapshot time in the ith observation time slot is shown,
Figure BDA0002679862900000023
the noise vector of the antenna array at the kth sampling moment of the ith observation time slot is M, the array element number is M, and the noise is assumed to be complex round white Gaussian noise which is independent from the signal.
As a further optimization scheme of the non-circular signal-oriented dimension reduction processing direct positioning method in the unmanned aerial vehicle mobile monitoring, the specific steps of expanding the received signal vector and calculating the expanded covariance matrix of the received signals of different observation time slots in the step 2) are as follows:
step 2.1), expanding a received signal vector according to the characteristics of the maximum non-circular rate signal:
Figure BDA0002679862900000024
in the formula, cl(k) For the extended received signal vector at the l-th observation slot, Al(p) is the direction matrix of the l-th observation slot,
Figure BDA0002679862900000025
in order to extend the direction matrix,
Figure BDA0002679862900000026
an extended direction vector for the l-th observation slot, al(pq) Is a vector of the direction of the light,
Figure BDA0002679862900000027
the non-circular phase of the qth radiation source, Q1, 2, …, Q,
Figure BDA0002679862900000028
in the form of a non-circular phase matrix,
Figure BDA0002679862900000029
a real envelope for the source signal vector;
step 2.2), calculating an extended covariance matrix of the received signal of each observation time slot according to the following formula:
Figure BDA00026798629000000210
in the formula (I), the compound is shown in the specification,
Figure BDA00026798629000000211
for the extended covariance matrix of the l-th observation slot,
Figure BDA00026798629000000212
and K is the sampling fast beat number.
As a further optimization scheme of the non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring, the cost function constructed by using a Capon algorithm in the step 2) is as follows:
Figure BDA00026798629000000213
in the formula (I), the compound is shown in the specification,
Figure BDA0002679862900000031
for the cost function before the dimensionality reduction,
Figure BDA0002679862900000032
for the extended signal manifold vector of the l-th observation slot in the search,
Figure BDA0002679862900000033
to expand the inverse of the covariance matrix, p is the position vector,
Figure BDA0002679862900000034
non-circular phase.
As a further optimization scheme of the non-circular signal-oriented dimension reduction processing direct positioning method in the unmanned aerial vehicle mobile monitoring, the detailed steps of the step 3) are as follows:
step 3.1), separating position information and noncircular phase information in the expanded received signal vector through matrix conversion:
Figure BDA0002679862900000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002679862900000036
for the qth spread signal manifold vector,
Figure BDA0002679862900000037
is a position information matrix of the qth radiation source,
Figure BDA0002679862900000038
for the non-circular phase information vector of the q-th radiation source,
Figure BDA0002679862900000039
is the non-circular phase of the qth radiation source;
for the l observation time slot, order
Figure BDA00026798629000000310
Then
Figure BDA00026798629000000311
And then to
Figure BDA00026798629000000312
Definition of
Figure BDA00026798629000000313
Then
Figure BDA00026798629000000314
For unknown parameters
Figure BDA00026798629000000315
The above equation is a quadratic optimization problem. Let e be [1,0 ]]TThen, then
Figure BDA00026798629000000316
The reconstruction optimization problem is then as follows:
Figure BDA00026798629000000317
solving by adopting a Lagrange multiplier method, and constructing the following functions:
Figure BDA00026798629000000318
in the formula (I), the compound is shown in the specification,
Figure BDA00026798629000000319
in order to be the objective function, the target function,
Figure BDA00026798629000000320
is a phase vector, JlAnd (p) is a position matrix corresponding to the l-th observation time slot, and lambda is a multiplier. Order the above type is to
Figure BDA00026798629000000321
Is zero, i.e.
Figure BDA00026798629000000322
Then
Figure BDA00026798629000000323
Where μ is the multiplier coefficient, Jl(p)-1Position matrix J corresponding to the l-th observation time slotl(p) the inverse;
and because of
Figure BDA0002679862900000041
Thus, μ 1/(e)HJl(p)-1e) Is thus
Figure BDA0002679862900000042
The child cost function of the l-th observation slot
Figure BDA0002679862900000043
Fusing the extended covariance matrix of all observation time slots to construct a reduced-dimension cost function fRD-Capon(p)：
Figure BDA0002679862900000044
As a further optimization scheme of the non-circular signal-oriented dimension reduction processing direct positioning method in the unmanned aerial vehicle mobile monitoring, the detailed steps of the step 4) are as follows:
and searching the cost function after dimension reduction, wherein the coordinates corresponding to the Q maximum peak values are the positions of the non-circular radiation sources.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the non-circular characteristic of the radiation source signal is utilized, and the positioning precision is effectively improved;
2. the degree of freedom of the algorithm is increased, and more information sources can be estimated simultaneously;
3. with higher source resolution.
Drawings
Fig. 1 is a flow chart of an implementation of a non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring provided by the invention;
FIG. 2 is a view of a multi-non-circular source positioning scenario in accordance with the present invention;
FIG. 3 is a positioning scattergram of the method of the present invention;
FIG. 4 is a comparison of the method of the present invention, the conventional Capon direct positioning algorithm and the two-step positioning algorithm without passing array elements;
FIG. 5 is a comparison of the method of the present invention, a conventional Capon direct localization algorithm and a two-step localization algorithm at different signal-to-noise ratios;
FIG. 6 is a comparison of the method of the present invention, the conventional Capon direct positioning algorithm and the two-step positioning algorithm at different snapshots;
FIG. 7 is a comparison chart of the calculation time before and after dimension reduction of the method of the present invention under different snapshot numbers.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, components are exaggerated for clarity.
As shown in fig. 1, a flow chart of a non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring is shown. The unmanned aerial vehicle receives signals from a plurality of non-circular radiation sources in L different observation time slots, and samples the received signals to obtain a received signal matrix; expanding a received signal matrix by using the characteristic that the elliptic covariance is not zero, calculating an expanded covariance matrix of the received signal, and establishing a cost function by using the concept of a Capon algorithm; reducing the dimension of the cost function, converting the cost function into a secondary optimization problem, and removing the non-circular phase search dimension; and finally, fusing covariance matrixes of L different observation time slot received signals, constructing a cost function after dimensionality reduction, and obtaining the position of the non-circular radiation source through searching, wherein the specific steps are as follows:
step 1: the unmanned aerial vehicle receives a plurality of non-circular radiation source signals at L different observation positions, and samples the received signals:
suppose that Q independent far-field narrow-band non-circular signals are incident to a motion observation platform carrying M-element uniform linear arrays, namely an unmanned aerial vehicle, and target sources are respectively positioned at pq＝[xq,yq]T(Q ═ 1,2, …, Q), the observation platform moves along a known trajectory, its multiple source localization scene graph based on non-circular signals is shown in fig. 2, the received signal of the observation platform at the kth (K ═ 1,2, …, L) observation position (K ═ 1,2, …, K) sampling moment is:
Figure BDA0002679862900000051
in the formula, rl(k) Is the received signal vector of the kth sampling moment of the l observation time slot, Q is the number of non-circular radiation sources,
Figure BDA0002679862900000052
for the signal manifold vector of the qth target source to the antenna array in the l observation time slot, sl,q(k) The signal waveform of the qth target source at the kth sampling snapshot time in the ith observation time slot is shown,
Figure BDA0002679862900000053
the noise vector of the antenna array in the l-th observation time slot is defined, M is the array element number, and the noise is assumed to be complex round white Gaussian noise independent from the signal.
Step 2: according to the non-circular characteristic of a signal source, expanding a received signal vector, respectively calculating an expanded covariance matrix of received signals of different observation time slots, and constructing a cost function by utilizing the idea of a Capon algorithm:
the characteristics of the maximum non-circular rate signal can be obtained as follows:
Figure BDA0002679862900000054
in the formula, sl(k) For the source signal vector of the l-th observation slot,
Figure BDA0002679862900000055
in the form of a non-circular phase matrix,
Figure BDA0002679862900000056
for the non-circular phase of the q-th radiation source,
Figure BDA0002679862900000061
a real envelope for the source signal vector;
thus, the spread received signal vector is:
Figure BDA0002679862900000062
in the formula, cl(k) For the extended received signal vector of the l-th observation slot, Al(p) is the direction matrix of the l-th observation slot,
Figure BDA0002679862900000063
in order to extend the direction matrix,
Figure BDA0002679862900000064
an extended direction vector for the l-th observation slot, al(pq) Is a direction vector.
The extended covariance matrix of the received signal for the ith observation slot
Figure BDA0002679862900000065
In the formula (I), the compound is shown in the specification,
Figure BDA0002679862900000066
and K is the matrix of the expanded received signals of the l-th observation time slot, and the sampling fast beat number is K.
Combining the idea of Capon algorithm in DOA estimation algorithm, the cost function is constructed as follows:
Figure BDA0002679862900000067
in the formula (I), the compound is shown in the specification,
Figure BDA0002679862900000068
for the cost function before the dimensionality reduction,
Figure BDA0002679862900000069
for the extended signal manifold vector of the l-th observation slot in the search,
Figure BDA00026798629000000610
to expand the inverse of the covariance matrix, p is the position vector,
Figure BDA00026798629000000611
non-circular phase.
And step 3: reducing the dimension of the cost function, and converting the non-circular phase dimension reduction problem into a secondary optimization problem:
in step 2, solving and searching dimensionality of the position of the radiation source is overlarge, reducing dimensionality and solving the dimensionality, rewriting the received signal vector in step 2, and separating position information from noncircular phase information through matrix conversion, wherein the method comprises the following steps:
Figure BDA00026798629000000612
in the formula，
Figure BDA00026798629000000613
For the qth spread signal manifold vector,
Figure BDA00026798629000000614
is a position information matrix of the qth radiation source,
Figure BDA00026798629000000615
for the non-circular phase information vector of the q-th radiation source,
Figure BDA00026798629000000616
is the non-circular phase of the qth radiation source;
for the l observation time slot, order
Figure BDA00026798629000000617
Then
Figure BDA00026798629000000618
And then to
Figure BDA00026798629000000619
Definition of
Figure BDA0002679862900000071
Then
Figure BDA0002679862900000072
For unknown parameters
Figure BDA0002679862900000073
The above equation is a quadratic optimization problem. Let e be [1,0 ]]TThen, then
Figure BDA0002679862900000074
The reconstruction optimization problem is then as follows:
Figure BDA0002679862900000075
adopting Lagrange multiplier method to solve and construct the following function
Figure BDA0002679862900000076
In the formula (I), the compound is shown in the specification,
Figure BDA0002679862900000077
in order to be the objective function, the target function,
Figure BDA0002679862900000078
is a phase vector, JlAnd (p) is a position matrix corresponding to the l-th observation time slot, and lambda is a multiplier. Order the above type is to
Figure BDA0002679862900000079
Is zero, i.e.
Figure BDA00026798629000000710
Then
Figure BDA00026798629000000711
Mu is the multiplier coefficient, Jl(p)-1Position matrix J corresponding to the l-th observation time slotl(p) the inverse;
and because of
Figure BDA00026798629000000712
Thus, μ 1/(e)HJl(p)-1e) Is thus
Figure BDA00026798629000000713
The sub-cost function of the ith slot
Figure BDA00026798629000000714
Fusing all the extended covariance matrixes to construct the matrix with reduced dimensionCost function fRD-Capon(p)：
Figure BDA00026798629000000715
And searching the position of the cost function, wherein the coordinates corresponding to the Q maximum peak values are the position of the non-circular radiation source.
The performance of the method of the invention is better than that of the traditional algorithm through simulation verification. Simulation analysis was performed using MATLAB with Root Mean Square Error (RMSE) as a criterion for evaluating performance, which is defined as follows:
Figure BDA00026798629000000716
wherein Q is the number of non-circular signal sources, MN is the number of Monte Carlo simulation experiments,
Figure BDA00026798629000000717
is an estimate of the location of the target source, (x)q,yq) Is the actual value of the target source location.
FIG. 3 is a positioning scattergram of the method of the present invention, wherein the number of radiation sources Q-3 is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,700](unit is m, the same below), non-circular phase
Figure BDA0002679862900000081
The unmanned aerial vehicle moves along a known track, a uniform linear array with the array element number M being 6 is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number K of each observation position is 100, and the signal-to-noise ratio is 5 dB. It can be seen from the figure that the present invention is effective in achieving simultaneous positioning of multiple non-circular radiation sources.
Fig. 4 is a comparison chart of the method of the present invention, the conventional Capon direct localization algorithm, and the conventional two-step localization algorithm without the array element number. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,700](unit is m, the same below), non-circular phase
Figure BDA0002679862900000082
The unmanned aerial vehicle moves along a known track, the number of array elements of the mounted uniform linear array is respectively 3, 5, 7 and 9, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number K of each observation position is 100, and the signal-to-noise ratio is 20 dB. As can be seen from the figure, the invention can still realize the positioning under the condition that the number of the array elements is equal to the number of the radiation sources, and the positioning precision is higher than that of the traditional Capon direct positioning algorithm and the two-step positioning algorithm.
FIG. 5 is a comparison graph of the method of the present invention, a conventional Capon direct localization algorithm, and a conventional two-step localization algorithm at different signal-to-noise ratios. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,700](unit is m, the same below), non-circular phase
Figure BDA0002679862900000083
The unmanned aerial vehicle moves along a known track, a uniform linear array with the array element number of 6 is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number K of each observation position is 200, and the signal-to-noise ratio is stepped from-5 dB to 30dB at intervals of 5 dB. As can be seen from the figure, the positioning performance of the method is always superior to that of the traditional Capon direct positioning algorithm and the two-step positioning algorithm as the signal-to-noise ratio is increased.
FIG. 6 is a comparison of the method of the present invention, a traditional Capon direct localization algorithm, and a traditional two-step localization algorithm at different snapshots. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,700](unit is m, the same below), non-circular phase
Figure BDA0002679862900000084
The unmanned aerial vehicle moves along a known track, the number of the mounted array elements is 6, and the number of the mounted array elements is 5, namely (-1000, -500), (-500, -5) observation positions00) (0, -500), (500, -500) and (1000, -500), the number of fast beats of samples for each observation position is stepped from 50 to 300 at 50 intervals, with a signal-to-noise ratio of 10 dB. As can be seen from the figure, with the increase of the number of snapshots, the positioning performance of the invention is continuously improved, and the positioning error is always smaller than that of the traditional Capon direct positioning algorithm and the two-step positioning algorithm.
FIG. 7 is a comparison chart of the method of the present invention before and after dimension reduction under different snapshot numbers. Assuming that the number of radiation sources Q is 3, each is located at p1＝[-800,800]、p2＝[0,500]And p3＝[800,700](unit is m, the same below), non-circular phase
Figure BDA0002679862900000091
The unmanned aerial vehicle moves along a known track, a uniform linear array with 6 array elements is mounted, 5 observation positions are respectively (-1000, -500), (-500 ), (0, -500), (500, -500) and (1000, -500), the sampling fast beat number of each observation position is from 50 to 300 in 50 intervals, and the signal-to-noise ratio is 20 dB. As can be seen from the figure, the dimension reduction method can effectively reduce the complexity of the algorithm and improve the practicability of the algorithm.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring is characterized by comprising the following steps:
step 1), an unmanned aerial vehicle receives a plurality of non-circular radiation source signals in L different observation time slots and samples the received signals;
step 2), expanding received signal vectors according to the non-circular characteristics of the signal source, respectively calculating expanded covariance matrixes of received signals of different observation time slots, and constructing a cost function by using a Capon algorithm;
step 3), reducing the dimension of the cost function, and converting the non-circular phase dimension reduction problem into a secondary optimization problem; fusing all the extended covariance matrixes, and constructing a cost function after dimension reduction;
and 4) searching the cost function subjected to the dimension reduction to obtain the position of the non-circular radiation source.
2. The method for non-circular signal-oriented dimension reduction processing direct positioning in unmanned aerial vehicle mobile monitoring according to claim 1, wherein in step 1), the received signal r of the unmanned aerial vehicle at the kth sampling moment of the ith observation time slotl(k) Is composed of
Figure FDA0002679862890000011
In the formula, rl(k) Is the received signal vector of the kth sampling moment of the l observation time slot, Q is the number of non-circular radiation sources,
Figure FDA0002679862890000012
for the signal manifold vector of the qth target source to the antenna array in the l observation time slot, sl,q(k) The signal waveform of the qth target source at the kth sampling snapshot time in the ith observation time slot is shown,
Figure FDA0002679862890000013
the noise vector of the antenna array for the kth sampling instant of the l-th observation slot,m is the array element number, and the noise is assumed to be complex round white Gaussian noise independent from the signal.
3. The non-circular signal-oriented dimension reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring according to claim 2, wherein the specific steps of expanding the received signal vector and calculating the expanded covariance matrix of the received signals of different observation time slots in step 2) are as follows:
step 2.1), expanding a received signal vector according to the characteristics of the maximum non-circular rate signal:
Figure FDA0002679862890000014
in the formula, cl(k) For the extended received signal vector at the l-th observation slot, Al(p) is the direction matrix of the l-th observation slot,
Figure FDA0002679862890000015
in order to extend the direction matrix,
Figure FDA0002679862890000016
an extended direction vector for the l-th observation slot, al(pq) Is a vector of the direction of the light,
Figure FDA0002679862890000017
the non-circular phase of the qth radiation source, Q1, 2, …, Q,
Figure FDA0002679862890000018
in the form of a non-circular phase matrix,
Figure FDA0002679862890000019
a real envelope for the source signal vector;
step 2.2), calculating an extended covariance matrix of the received signal of each observation time slot according to the following formula:
Figure FDA0002679862890000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002679862890000022
for the extended covariance matrix of the l-th observation slot,
Figure FDA0002679862890000023
and K is the sampling fast beat number.
4. The non-circular signal-oriented dimensionality reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring according to claim 3, wherein the cost function constructed by using a Capon algorithm in the step 2) is as follows:
Figure FDA0002679862890000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002679862890000025
for the cost function before the dimensionality reduction,
Figure FDA0002679862890000026
for the extended signal manifold vector of the l-th observation slot in the search,
Figure FDA0002679862890000027
to expand the inverse of the covariance matrix, p is the position vector,
Figure FDA0002679862890000028
non-circular phase.
5. The non-circular signal-oriented dimensionality reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring according to claim 4, wherein the detailed steps of the step 3) are as follows:
step 3.1), separating position information and noncircular phase information in the expanded received signal vector through matrix conversion:
Figure FDA0002679862890000029
in the formula (I), the compound is shown in the specification,
Figure FDA00026798628900000210
for the qth spread signal manifold vector,
Figure FDA00026798628900000211
is a position information matrix of the qth radiation source,
Figure FDA00026798628900000212
for the non-circular phase information vector of the q-th radiation source,
Figure FDA00026798628900000213
is the non-circular phase of the qth radiation source;
for the l observation time slot, order
Figure FDA00026798628900000214
Then
Figure FDA00026798628900000215
And then to
Figure FDA00026798628900000216
Definition of
Figure FDA00026798628900000217
Then
Figure FDA00026798628900000218
For unknown parameters
Figure FDA00026798628900000219
The above equation is a quadratic optimization problem. Let e be [1,0 ]]TThen, then
Figure FDA00026798628900000220
The reconstruction optimization problem is then as follows:
Figure FDA00026798628900000221
solving by adopting a Lagrange multiplier method, and constructing the following functions:
Figure FDA0002679862890000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002679862890000032
in order to be the objective function, the target function,
Figure FDA0002679862890000033
is a phase vector, JlAnd (p) is a position matrix corresponding to the l-th observation time slot, and lambda is a multiplier. Order the above type is to
Figure FDA0002679862890000034
Is zero, i.e.
Figure FDA0002679862890000035
Then
Figure FDA0002679862890000036
Where μ is the multiplier coefficient, Jl(p)-1Position matrix J corresponding to the l-th observation time slotl(p) the inverse;
and because of
Figure FDA0002679862890000037
Thus, μ 1/(e)HJl(p)-1e) Is thus
Figure FDA0002679862890000038
The child cost function for the ith observation slot is then:
Figure FDA0002679862890000039
fusing the extended covariance matrix of all observation time slots to construct a reduced-dimension cost function fRD-Capon(p)：
Figure FDA00026798628900000310
6. The non-circular signal-oriented dimensionality reduction processing direct positioning method in unmanned aerial vehicle mobile monitoring according to claim 5, wherein the detailed steps of the step 4) are as follows:
and searching the cost function after dimension reduction, wherein the coordinates corresponding to the Q maximum peak values are the positions of the non-circular radiation sources.
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